EFFICIENT NUMERICAL SOLUTION OF TWO-DIMENSIONAL TIME-SPACE FRACTIONAL NONLINEAR DIFFUSION-WAVE EQUATIONS WITH INITIAL SINGULARITY

In this paper, we present an efficient linearized alternating direction implicit (ADI) scheme for two-dimensional time-space fractional nonlinear diffusion-wave equations with initial singularity. First, the original problem is equivalently transformed into its partial integro-differential form. Then, for the time discretization, the Crank-Nicolson technique combined with the midpoint formula and the second order convolution quadrature formula are used. Meanwhile, the classical central difference formula and fractional central difference formula are adopted to approximate the second order derivative and the Riesz derivative in space, respectively. The unconditional stability and convergence of the proposed scheme are proved by the energy method. Numerical experiments support the theoretical results.